MathDB
Orthocenter

Source: Chinese TST

April 4, 2008
geometrycircumcirclegeometric transformationreflectiongeometry proposed

Problem Statement

Let ABC ABC be a triangle, line l l cuts its sides BC,CA,AB BC,CA,AB at D,E,F D,E,F, respectively. Denote by O1,O2,O3 O_{1},O_{2},O_{3} the circumcenters of triangle AEF,BFD,CDE AEF,BFD,CDE, respectively. Prove that the orthocenter of triangle O1O2O3 O_{1}O_{2}O_{3} lies on line l l.
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